tikz

TikZ/PGF — Vector Graphics & Diagrams

CTAN: https://ctan.org/pkg/pgf
Manual: texdoc tikz (~1300 pages)

Setup

\usepackage{tikz}
% Load libraries as needed:
\usetikzlibrary{arrows.meta, calc, positioning, decorations.pathmorphing,
  patterns, shapes.geometric, shapes.misc, fit, backgrounds,
  automata, trees, mindmap, circuits.logic.US}

Basic Drawing

Minimal Example

\begin{tikzpicture}
  \draw (0,0) -- (2,0) -- (2,2) -- cycle;  % triangle
\end{tikzpicture}

Path Operations

Operation	Syntax	Example
Line	--	(0,0) -- (1,1)
Horizontal-vertical	<code>-|</code>	`(0,0) -
Vertical-horizontal	<code>|-</code>	`(0,0)
Curve	.. controls .. ..	(0,0) .. controls (0.5,1) .. (1,0)
Smooth curve	to[out=..,in=..]	(0,0) to[out=90,in=180] (2,1)
Arc	arc	(0,0) arc (0:90:1cm) start:end:radius
Circle	circle	(0,0) circle[radius=1]
Ellipse	ellipse	(0,0) ellipse[x radius=2, y radius=1]
Rectangle	rectangle	(0,0) rectangle (2,1)
Grid	grid	(0,0) grid (3,3)
Parabola	parabola	(0,0) parabola (2,2)
Sin/Cos	sin/cos	(0,0) sin (1,1)
Plot	plot	plot[domain=0:3] (\x, {\x^2})
Cycle	cycle	close path back to start

Path Actions

Command	Effect
\draw	Stroke the path
\fill	Fill the path
\filldraw	Fill and stroke
\path	Invisible path (for coordinates, nodes)
\clip	Clip subsequent drawing to path
\shade	Gradient fill
\shadedraw	Gradient fill + stroke
\node	Shorthand for \path node
\coordinate	Shorthand for \path coordinate

Common Draw Options

\draw[
  color=blue,            % or just: blue
  line width=1pt,        % or: thin, thick, very thick, ultra thick
  dashed,                % or: dotted, dash dot, dash dot dot
  dash pattern={on 3pt off 2pt},
  rounded corners=5pt,
  ->                     % arrow tip (see arrows section)
  opacity=0.5,
  double,
  double distance=2pt,
] (0,0) -- (2,2);

Common Fill Options

\fill[
  fill=blue!20,          % 20% blue
  fill opacity=0.5,
  pattern=north lines,   % requires patterns library
  pattern color=gray,
] (0,0) rectangle (2,1);

Coordinate Systems

% Cartesian (default)
(2, 3)

% Polar (angle:radius)
(45:2cm)

% Relative (shift from last point)
++(1,0)    % move reference point
+(1,0)     % don't move reference point

% Named
\coordinate (A) at (1,2);
\draw (A) -- (2,3);

% Intersection (calc library)
\usetikzlibrary{calc}
($(A)!0.5!(B)$)           % midpoint of A and B
($(A)!0.5!90:(B)$)        % midpoint rotated 90°
($(A) + (1,2)$)           % A shifted by (1,2)
($(A)!1cm!(B)$)           % 1cm from A toward B

% Perpendicular coordinates (A -| B) = (x of B, y of A)
(A |- B)                   % (x of A, y of B)

% Barycentric
(barycentric cs:A=1,B=1,C=1)  % centroid

Nodes

Basic Nodes

\node (name) at (0,0) {Text};

% Node options
\node[
  draw,                    % draw border
  fill=yellow!20,
  rectangle,               % shape (default)
  circle,
  ellipse,
  rounded corners,
  minimum width=2cm,
  minimum height=1cm,
  inner sep=5pt,           % padding
  outer sep=2pt,           % margin
  text=red,
  font=\bfseries\small,
  align=center,            % for multi-line: use \\ in text
  text width=3cm,
  anchor=north,            % positioning anchor
  rotate=45,
] (mynode) at (1,2) {Hello\\World};

Node Anchors

          north west  north  north east
                 ┌──────────┐
            west │  center   │ east
                 └──────────┘
          south west  south  south east

Also: base, mid, text, and angle anchors like 45, 135.

Nodes on Paths

\draw (0,0) -- node[above] {label} (3,0);
\draw (0,0) -- node[midway, sloped, above] {sloped text} (3,2);
\draw (0,0) -- node[pos=0.3, below] {at 30\%} (3,0);
\draw (0,0) to[out=90,in=0] node[near start, left] {A} (2,2);

Common Shapes (requires libraries)

\usetikzlibrary{shapes.geometric, shapes.misc}

\node[diamond, draw] {D};
\node[star, draw, star points=5] {S};
\node[regular polygon, regular polygon sides=6, draw] {Hex};
\node[trapezium, draw] {T};
\node[cylinder, draw, shape border rotate=90] {DB};
\node[cloud, draw, cloud puffs=10] {Cloud};
\node[cross out, draw] at (0,0) {};
\node[strike out, draw] at (0,0) {};

Arrows

\usetikzlibrary{arrows.meta}

% Arrow tips (arrows.meta syntax)
\draw[->] (0,0) -- (1,0);              % default
\draw[-Stealth] (0,0) -- (1,0);        % filled triangle
\draw[-Latex] (0,0) -- (1,0);          % larger filled
\draw[-{Stealth[length=5mm]}] (0,0) -- (1,0);
\draw[{Latex[red]}-{Latex[blue]}] (0,0) -- (1,0);  % colored
\draw[-{>[scale=2]}] (0,0) -- (1,0);

% Common tips: >, Stealth, Latex, To, Circle, Square, |, Hooks
% Modifiers: [length=..], [width=..], [open], [fill=..], [scale=..]

Styles

% Define in preamble or tikzpicture options
\tikzset{
  mybox/.style = {draw, fill=blue!20, rounded corners, minimum width=2cm},
  myarrow/.style = {-Stealth, thick, red},
  highlight/.style = {fill=yellow, draw=orange, line width=2pt},
}

% Use
\node[mybox] {Box};
\draw[myarrow] (0,0) -- (1,1);

% Style with parameters
\tikzset{
  box/.style = {draw, fill=#1!20, minimum width=1.5cm},
  box/.default = blue,
}
\node[box] {Blue};        % default
\node[box=red] {Red};     % override

% every node/.style applies to all nodes
\begin{tikzpicture}[every node/.style={font=\small}]

Foreach Loops

% Basic
\foreach \x in {0,1,2,3}
  \draw (\x, 0) circle (0.3);

% With step
\foreach \x in {0,0.5,...,3}
  \fill (\x,0) circle (1pt);

% Multiple variables
\foreach \x/\y in {0/A, 1/B, 2/C}
  \node at (\x, 0) {\y};

% Counter
\foreach \x [count=\i] in {a,b,c,d}
  \node at (\i, 0) {\x};

% Evaluate
\foreach \x [evaluate=\x as \y using \x*\x] in {1,...,5}
  \fill (\x, \y/5) circle (2pt);

% Remember
\foreach \x [remember=\x as \lastx (initially 0)] in {1,...,5}
  \draw (\lastx, 0) -- (\x, 0);

Scopes and Transformations

\begin{tikzpicture}
  \draw (0,0) -- (1,0);
  
  \begin{scope}[shift={(2,0)}, rotate=45, scale=0.5, red, thick]
    \draw (0,0) -- (1,0) -- (1,1) -- cycle;
  \end{scope}
  
  % Transformations
  % shift={(x,y)}, xshift=1cm, yshift=2cm
  % rotate=45, rotate around={45:(1,1)}
  % scale=2, xscale=2, yscale=0.5
  % xslant=0.5, yslant=0.5
\end{tikzpicture}

Clipping

\begin{tikzpicture}
  \clip (0,0) circle (1.5cm);
  % Everything below is clipped to the circle
  \fill[blue!30] (-2,-2) rectangle (2,2);
  \draw[step=0.5, gray] (-2,-2) grid (2,2);
\end{tikzpicture}

Layers (backgrounds library)

\usetikzlibrary{backgrounds}

\begin{tikzpicture}
  \node[draw, fill=white] (A) {Foreground};
  
  \begin{pgfonlayer}{background}
    \fill[yellow!30] (A.south west) rectangle (A.north east);
  \end{pgfonlayer}
\end{tikzpicture}

Pics

\tikzset{
  myshape/.pic = {
    \draw (-0.5,-0.5) rectangle (0.5,0.5);
    \draw (0,0) circle (0.3);
  }
}

\begin{tikzpicture}
  \pic at (0,0) {myshape};
  \pic[rotate=45, scale=1.5] at (2,0) {myshape};
\end{tikzpicture}

Decorations

\usetikzlibrary{decorations.pathmorphing, decorations.markings, decorations.text}

% Wavy/zigzag lines
\draw[decorate, decoration={zigzag, amplitude=2mm, segment length=5mm}]
  (0,0) -- (4,0);
\draw[decorate, decoration={snake, amplitude=1mm}]
  (0,0) -- (4,0);
\draw[decorate, decoration={coil, aspect=0.5}]
  (0,0) -- (4,0);
\draw[decorate, decoration={random steps, segment length=3mm}]
  (0,0) -- (4,0);

% Brace
\draw[decorate, decoration={brace, amplitude=5pt}]
  (0,0) -- (3,0) node[midway, above=5pt] {label};

% Text along path
\draw[decorate, decoration={text along path, text={Hello World}}]
  (0,0) .. controls (1,1) .. (3,0);

% Markings (arrows along path)
\draw[decoration={markings, mark=at position 0.5 with {\arrow{>}}},
  postaction={decorate}]
  (0,0) -- (3,0);

Patterns

\usetikzlibrary{patterns}

\fill[pattern=north east lines] (0,0) rectangle (2,1);
\fill[pattern=crosshatch dots, pattern color=blue] (0,0) circle (1);

% Available: north east lines, north west lines, horizontal lines,
% vertical lines, crosshatch, dots, crosshatch dots,
% fivepointed stars, sixpointed stars, bricks, checkerboard

---

Common Diagram Patterns

Flowchart

\usetikzlibrary{arrows.meta, shapes.geometric, positioning}

\tikzset{
  startstop/.style = {rectangle, rounded corners, draw, fill=red!20,
    minimum width=3cm, minimum height=1cm},
  process/.style = {rectangle, draw, fill=blue!20,
    minimum width=3cm, minimum height=1cm},
  decision/.style = {diamond, draw, fill=green!20,
    minimum width=3cm, minimum height=1cm, aspect=1.5},
  io/.style = {trapezium, trapezium left angle=70, trapezium right angle=110,
    draw, fill=orange!20, minimum width=3cm, minimum height=1cm},
  arrow/.style = {thick, -Stealth},
}

\begin{tikzpicture}[node distance=1.5cm]
  \node[startstop] (start) {Start};
  \node[io, below=of start] (input) {Input $x$};
  \node[decision, below=of input] (decide) {$x > 0$?};
  \node[process, below left=of decide] (neg) {$y = -x$};
  \node[process, below right=of decide] (pos) {$y = x$};
  \node[io, below=2cm of decide] (output) {Output $y$};
  \node[startstop, below=of output] (stop) {Stop};

  \draw[arrow] (start) -- (input);
  \draw[arrow] (input) -- (decide);
  \draw[arrow] (decide) -| node[near start, above] {No} (neg);
  \draw[arrow] (decide) -| node[near start, above] {Yes} (pos);
  \draw[arrow] (neg) |- (output);
  \draw[arrow] (pos) |- (output);
  \draw[arrow] (output) -- (stop);
\end{tikzpicture}

Tree

\begin{tikzpicture}[
  level 1/.style={sibling distance=4cm},
  level 2/.style={sibling distance=2cm},
  every node/.style={draw, circle, minimum size=8mm},
  edge from parent/.style={draw, -Stealth},
]
  \node {1}
    child { node {2}
      child { node {4} }
      child { node {5} }
    }
    child { node {3}
      child { node {6} }
      child { node {7} }
    };
\end{tikzpicture}

Graph / Network

\usetikzlibrary{positioning}

\begin{tikzpicture}[
  vertex/.style={draw, circle, fill=blue!20, minimum size=8mm},
  edge/.style={thick},
  >=Stealth,
]
  \node[vertex] (a) at (0,2)  {A};
  \node[vertex] (b) at (2,3)  {B};
  \node[vertex] (c) at (4,2)  {C};
  \node[vertex] (d) at (2,0)  {D};

  \draw[edge] (a) -- node[above left]  {3} (b);
  \draw[edge] (b) -- node[above right] {2} (c);
  \draw[edge] (a) -- node[below left]  {7} (d);
  \draw[edge] (c) -- node[below right] {1} (d);
  \draw[edge] (b) -- node[right]       {4} (d);
\end{tikzpicture}

Finite Automaton / State Machine

\usetikzlibrary{automata, positioning}

\begin{tikzpicture}[shorten >=1pt, node distance=2.5cm, on grid, auto,
  every state/.style={draw, minimum size=1cm}]

  \node[state, initial]           (q0) {$q_0$};
  \node[state, right=of q0]      (q1) {$q_1$};
  \node[state, accepting, right=of q1] (q2) {$q_2$};

  \path[->]
    (q0) edge              node {a}   (q1)
    (q0) edge [loop above] node {b}   ()
    (q1) edge              node {a,b} (q2)
    (q1) edge [bend left]  node {b}   (q0)
    (q2) edge [loop above] node {a}   ();
\end{tikzpicture}

Mind Map

\usetikzlibrary{mindmap}

\begin{tikzpicture}[mindmap, grow cyclic,
  every node/.style={concept, execute at begin node=\hskip0pt},
  concept color=blue!40,
  level 1/.append style={level distance=4cm, sibling angle=90},
  level 2/.append style={level distance=2.5cm, sibling angle=45},
]
  \node {Main Topic}
    child[concept color=red!40] { node {Sub 1}
      child { node {Detail A} }
      child { node {Detail B} }
    }
    child[concept color=green!40] { node {Sub 2}
      child { node {Detail C} }
    }
    child[concept color=orange!40] { node {Sub 3} }
    child[concept color=purple!40] { node {Sub 4} };
\end{tikzpicture}

Block Diagram / System Diagram

\usetikzlibrary{positioning, arrows.meta, fit}

\begin{tikzpicture}[
  block/.style={draw, rectangle, fill=blue!10, minimum height=1cm,
    minimum width=2cm, align=center},
  sum/.style={draw, circle, minimum size=6mm},
  >=Stealth, thick,
]
  \node[sum] (sum) {};
  \node[block, right=1.5cm of sum] (ctrl) {Controller\\$G_c(s)$};
  \node[block, right=1.5cm of ctrl] (plant) {Plant\\$G(s)$};
  \node[block, below=1cm of plant] (fb) {Sensor\\$H(s)$};

  \draw[->] ++(-1.5,0) -- node[above] {$R(s)$} (sum);
  \draw[->] (sum) -- node[above] {$E(s)$} (ctrl);
  \draw[->] (ctrl) -- (plant);
  \draw[->] (plant) -- ++(2,0) node[above left] {$Y(s)$};
  \draw[->] (plant.east) ++(1,0) |- (fb);
  \draw[->] (fb) -| (sum) node[near end, left] {$-$};

  \node at (sum) {$\Sigma$};
\end{tikzpicture>

Venn Diagram

\begin{tikzpicture}
  \fill[red!20]  (0,0)   circle (1.5cm);
  \fill[blue!20] (1.5,0) circle (1.5cm);
  
  \begin{scope}
    \clip (0,0) circle (1.5cm);
    \fill[purple!30] (1.5,0) circle (1.5cm);
  \end{scope}
  
  \draw (0,0) circle (1.5cm) node[left=1cm]  {$A$};
  \draw (1.5,0) circle (1.5cm) node[right=1cm] {$B$};
  \node at (0.75, 0) {$A \cap B$};
\end{tikzpicture}

Timeline

\begin{tikzpicture}
  \draw[thick, -Stealth] (0,0) -- (10,0);
  
  \foreach \x/\year/\event in {
    1/2020/Founded,
    3/2021/v1.0,
    5.5/2022/IPO,
    8/2023/Global%
  }{
    \draw (\x, -0.15) -- (\x, 0.15);
    \node[above=3pt] at (\x, 0.15) {\footnotesize \year};
    \node[below=3pt, align=center, text width=1.5cm] at (\x, -0.15) {\footnotesize \event};
  }
\end{tikzpicture}

Circuit (Logic Gates)

\usetikzlibrary{circuits.logic.US}

\begin{tikzpicture}[circuit logic US, every circuit symbol/.style={thick}]
  \node[and gate] (and1) at (2,1) {};
  \node[or gate]  (or1)  at (4,0.5) {};

  \draw (0,1.25) node[left] {$A$} -- (and1.input 1);
  \draw (0,0.75) node[left] {$B$} -- (and1.input 2);
  \draw (and1.output) -- (or1.input 1);
  \draw (0,0)    node[left] {$C$} -- (or1.input 2);
  \draw (or1.output) -- ++(1,0) node[right] {$Y$};
\end{tikzpicture}

Commutative Diagram (Math)

\usetikzlibrary{positioning}

\begin{tikzpicture}[>=Stealth, node distance=2cm]
  \node (A)              {$A$};
  \node (B) [right=of A] {$B$};
  \node (C) [below=of A] {$C$};
  \node (D) [right=of C] {$D$};

  \draw[->] (A) -- node[above] {$f$} (B);
  \draw[->] (A) -- node[left]  {$g$} (C);
  \draw[->] (B) -- node[right] {$h$} (D);
  \draw[->] (C) -- node[below] {$k$} (D);
\end{tikzpicture}

Plot (built-in, no pgfplots)

\begin{tikzpicture}[scale=0.8]
  \draw[->] (-0.5,0) -- (4.5,0) node[right] {$x$};
  \draw[->] (0,-0.5) -- (0,3.5) node[above] {$y$};
  
  \draw[blue, thick, domain=0:4, samples=100]
    plot (\x, {sqrt(\x)});
  
  \foreach \x in {1,...,4}
    \draw (\x, 0.1) -- (\x, -0.1) node[below] {\x};
  \foreach \y in {1,2,3}
    \draw (0.1, \y) -- (-0.1, \y) node[left] {\y};
\end{tikzpicture}

Positioning Library

\usetikzlibrary{positioning}

% Relative positioning (preferred over manual coordinates)
\node[right=of A] (B) {B};       % default separation
\node[right=1.5cm of A] (B) {B}; % custom distance
\node[above right=1cm and 2cm of A] (B) {B};  % separate x/y

% Available: above, below, left, right,
% above left, above right, below left, below right

Fit Library

\usetikzlibrary{fit}

% Draw a box around multiple nodes
\node[draw, dashed, fit=(A) (B) (C), inner sep=5pt, label=above:Group] {};

Calc Library Key Operations

\usetikzlibrary{calc}

% Midpoint
($(A)!0.5!(B)$)

% Point 1cm from A toward B
($(A)!1cm!(B)$)

% Projection of C onto line AB
($(A)!(C)!(B)$)

% Rotated point: midpoint of AB rotated 90° around A
($(A)!0.5!90:(B)$)

% Vector addition
($(A) + (1,2)$)

% Scalar multiply
($2*(A) - (B)$)

% let syntax for complex calculations
\draw let \p1 = ($(B)-(A)$),
          \n1 = {veclen(\x1,\y1)}
      in (A) circle (\n1);

Externalizing (Caching) Figures

% In preamble — compiles each tikzpicture once, reuses PDF
\usetikzlibrary{external}
\tikzexternalize[prefix=tikz-cache/]

% To skip a figure:
\tikzexternaldisable
\begin{tikzpicture} ... \end{tikzpicture}
\tikzexternalenable

Requires --shell-escape flag: pdflatex --shell-escape main.tex

Common Pitfalls

Problem	Cause	Fix
"Dimension too large"	Coordinates too big	Use scale or smaller coords
Missing arrow tips	Forgot arrows.meta library	\usetikzlibrary{arrows.meta}
Node text cut off	Node too small	Add minimum width, text width
positioning not working	Forgot library	\usetikzlibrary{positioning}
Nodes overlap	Using at instead of relative	Use right=of with positioning lib
foreach errors	Special chars in body	Wrap body in {}
Path not closing	Forgot cycle	End path with -- cycle
Slow compilation	Complex figures	Use external library for caching
Math in nodes	$ conflicts	Use $...$ inside node text normally
Colors not found	Missing xcolor	TikZ loads xcolor; use \usepackage[dvipsnames]{xcolor} before tikz for extra colors

Tips

• Use positioning library — never hardcode coordinates for node layouts
• \tikzset in preamble for reusable styles across figures
• every node/.style, every path/.style for consistent appearance
• Use \begin{scope} to limit option scope
• name path=X + name intersections (intersections library) to find crossing points
• For standalone figures: \documentclass[tikz]{standalone}
• spy library for magnification insets
• pgfplotstable for data-driven diagrams (see pgfplots skill)